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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
If x > 0, x/|x| < x is equivalent to x/x < x or x > 1.
If x < 0, x/|x| < x is equivalent to x/(-x) < x or x > -1, and we have -1 < x < 0.
In inequality questions, the law "Question is King" tells us that if the solution set of the question does not include the solution set of a condition, then the condition is not sufficient.
Since the solution of the question does not include that of condition 1), condition 1) is not sufficient.

Condition 2)
x=|x| is equivalent to x ≥ 0.
Since x is not 0, we must have x > 0.
Since the solution set of the question does not include the solution set of condition 2), condition 2) is not sufficient.

Conditions 1) & 2)
Condition 1) yields x > 1 or -1 < x < 0, while condition 2) yields x > 0.
Thus, applying both conditions together yields x > 0.
Since the solution set of the question does not include the solution set of both conditions, taken together, they are not sufficient.

Therefore, C is the answer.
Answer: C

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.